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VOL. 30 | 2001 Class Field Theory in Characteristic $p$, its Origin and Development


Today’s notion of “global field” comprises number fields (algebraic, of finite degree) and function fields (algebraic, of dimension 1, finite base field). They have many similar arithmetic properties. The systematic study of these similarities seems to have been started by Dedekind (1857). A new impetus was given by the seminal thesis of E.Artin (1921, published in 1924). In this exposition I shall report on the development during the twenties and thirties of the 20th century, with emphasis on the emergence of class field theory for function fields. The names of F.K.Schmidt, H. Hasse, E. Witt, C. Chevalley (among others) are closely connected with that development.


Published: 1 January 2001
First available in Project Euclid: 13 September 2018

zbMATH: 1068.11073
MathSciNet: MR1846477

Digital Object Identifier: 10.2969/aspm/03010549

Rights: Copyright © 2001 Mathematical Society of Japan


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